Swordfish

What is a Swordfish?

A Swordfish is an X-Wing with three lines instead of two. Take one digit. If, in three rows, every place the digit can go falls within the same three columns, then those rows put their three copies of the digit into those three columns, one in each. Every other cell in the three columns loses the digit.

Each row may have two or three spots; the pattern does not need all nine corners of the shape. As with an X-Wing, it also works with rows and columns swapped.

How to spot a Swordfish

Highlight one digit and list, for each row, the columns where it can go. Keep the rows with two or three spots. If three of them use only three columns between them, that is a Swordfish; clear the digit from the rest of those columns. Then repeat with columns in place of rows.

It is rarer than an X-Wing and harder to see, because the shape is not a rectangle. Writing the column numbers down for each row is the reliable way to find one.

A worked example

Cells are named by row and column: r4c1 is row 4, column 1. Rows count from the top, columns from the left, and boxes are numbered 1 to 9 reading like a book, so box 1 is top-left and box 9 is bottom-right.

This position is from an Expert puzzle our game dealt. Every candidate is pencilled in from the digits on the board; the diagram shows only the 2s. Nothing simpler moves it forward, an X-Wing and an XY-Wing included.

Look at rows 2, 6 and 7. In row 2 the 2 can go in columns 1, 2 or 7; in row 6, in columns 2 or 7; in row 7, in columns 1 or 2. That is three rows and, between them, only columns 1, 2 and 7. Each row needs its own 2 and no two of them can share a column, so the three 2s fill columns 1, 2 and 7, one each.

That leaves no room for another 2 in those columns. Column 1 loses it from r3c1 and r4c1, and column 7 from r4c7. r4c7 held only 2 and 7, so r4c7 is 7.

Why it works

Three rows need three 2s, and all their spots are in three columns, so the columns are shared out among them: each of columns 1, 2 and 7 receives exactly one 2 from those rows. A 2 anywhere else in those columns would be a second 2 in its column.

Which difficulty levels need it

Expert only. Our game's own solver stops at naked pairs, and any puzzle it cannot finish with those is rated Expert, so no Easy, Medium or Hard puzzle needs a Swordfish.

We measured 3,000 Expert puzzles our generator dealt. A solver that always tries the simplest technique first made a move with a Swordfish in 100 of them. For 13 (0.4%), the Swordfish was the hardest technique the puzzle needed: everything simpler stalls, and adding it finishes the grid. Of the 719 puzzles that the twelve techniques in this guide finish on their own, 11 cannot be finished without it. The rest of our Expert puzzles need techniques this guide does not cover yet, almost all of them chains.

Related: X-Wing .